Solver neutral element quality checks

For the following solvers, you can use the options in the Element Quality dialog box to perform some general checks of element quality based on a general set of solver neutral criteria:

• Simcenter 3D Thermal/Flow

• Simcenter 3D Electronic Systems Cooling

• Simcenter 3D Space Systems Thermal

• Simcenter 3D Acoustics BEM

• I-deas Universal File

• SC03

Aspect Ratio

The Aspect Ratio check measures the ratio of an element's length to its width.

Triangular element aspect ratio

For triangular elements, the software uses a two-step process to evaluate the aspect ratio.

• The software first calculates the ratio of the length of the each edge (H2) to the height (H1) of each of the triangle’s altitudes.The software multiplies this ratio (H2/H1) d\ by SQRT(3)/2, such that the aspect ratio for an element in the shape of an equilateral triangle equals 1. The software inverts this ratio if it is less than 1.0.The software performs this calculation for each edge and produces three values.

• The software then performs the second calculation, which is illustrated in the following graphic.where:N1, N2, and N3 are the first, second, and third nodes of the triangular element.x1 and x3 are the edge bisector points for edges 1 and 3, respectively.m13 is the triangle median that connects x1 and N3.p1 = the intersection of m13 with the line that is perpendicular to m13 that passes through point x3.For each edge, the software computes:L1, which is the length of m13. The software then multiplies that length by √3/2, such that the aspect ratio for an element in the shape of an equilateral triangle equals 1.L2, which is the length from x3 to p1. The software then multiplies that distance by 4.0 such that the aspect ratio for an element in the shape of an equilateral triangle equals 1.(L1*√3/2 )/(L2*4), which is the aspect ratio. The software inverts this ratio if it is less than 1.0.The software performs this calculation for each edge and produces three values.

The final aspect ratio for the element is the maximum of the six computed values.

Quadrilateral element aspect ratio

The aspect ratio for a quad element is determined using a test proposed by Robinson and Haggenmacher (NOTE). This test is based on a projection plane created by first bisecting the four element edges, then creating a point on the plane at the vector average of the corners. The X-axis extends from the point to the bisector on edge 2. The ratio is determined as the ratio of the length from the origin to the bisector of edge 2 to the length from the origin to the bisector of edge 3. If the ratio is less than 1.0, it is inverted.

Tetrahedral element aspect ratio

The aspect ratio for a tetrahedral element is computed by taking the ratio of the height of a vertex to the square root of the area of the opposing face.

The maximum height to area value is multiplied by a factor cf = 0.805927, which is the ratio of height to edge length for an equilateral tetrahedron. This result is the aspect ratio. With an equilateral tetrahedral element, the software reports a value of 1.

Aspect ratio = Max(cf(hi)/sqrt(Ai)), where i = 1,2,3,4.

Pyramid element aspect ratio

The software calculates the aspect ratio for a pyramid element by splitting the pyramid element into four tetrahedral elements with two diagonals on the quadrilateral face. The aspect ratio for the pyramid element is the maximum aspect ratio of each of the four tetrahedral elements.

Wedge element aspect ratio

The aspect ratio for a wedge element is determined by obtaining the midsurface for the wedge element. The software obtains this midsurface by averaging the two triangular faces of the wedge element where:

• h1 is the height of the wedge element, which is the distance of the center points on two triangular faces.

• h2 is the maximum edge length of the midsurface.

The software then calculates the aspect ratio as follows:

• If h1 > h2, the aspect ratio equals the midsurface aspect ratio multiplied by h1/h2.

• If h1 < h2, the aspect ratio equals either the midsurface aspect ratio or h2/h1, whichever is greater.

Hexahedral element aspect ratio

The aspect ratio for a hexahedral element is calculated as the ratio of the distance between opposing faces. This distance is determined by treating each hexahedral face as if it were a warped quadrilateral element. The software:

1. Processes each face to produce a projected plane.

2. Compares the distances between the center points of all three pairs of opposing faces.

3. Determines the aspect ratio by taking the maximum distance between any two faces and dividing it by the minimum distance between any two faces.

Warp

The Warp check measures the out-of-plane deviation of an element.

Quadrilateral warp

For quadrilateral elements, the software uses a test proposed by Robinson and Haggenmacher to calculate the warp value. The test is based on a projection plane created by first bisecting the four element edges, and then creating a point on the plane at the vector average of the corners (where the X-axis extends from the point to the bisector on edge 2). The plane normal is in the direction of the cross product of the X-axis and the vector from the origin to the bisector of edge 3. Every corner of the quad is a distance h from the plane. The length of each half edge is measured and the shortest length is assigned a value of 1. The warp angle is the arcsine of the ratio of the projection height h to the half edge length 1.

Wedge and hexahedral warp

The software evaluates each face of a wedge or hexahedral element for warp as if it were a quadrilateral element. The software retains the highest resulting angle for each element as the warp angle.

Skew

The Skew check measures the angular deviation of an element using an edge bisector method.

Triangular skew angle

Three potential skew angles are computed for each triangular element. To calculate each skew angle, the software constructs two vectors: one from a vertex to the mid-point of the opposite edge; the other between the mid-points of the adjacent edges. The software subtracts the angle between these two vectors from 90°:

skew angle = |90°–a|.

This procedure is repeated for the other two vertices. The largest of the three computed angles is the skew angle for that element. The skew factor is computed as:

|90°–a|/90°

Quadrilateral skew angle

Prior to testing for skew, the software checks each element for convexity. Elements which fail the convexity check double-back on themselves. This causes the element stiffness terms to contain either a zero or negative value.

The following graphic shows examples of (A) a quadrilateral element with incorrect nodal sequencing, or a double-reentrant angle, and (B) a quadrilateral element with a single reentrant angle.

The Skew check is based on a reference frame created by first bisecting the four element edges, then creating an origin at the vector average of the corners (where the X-axis extends from the origin to the bisector on edge 2). The Z-axis is in the direction of the cross product of the X-axis and the vector from the origin to the bisector of edge 3. The Y-axis is in the direction of the live cross product of the X- and Z-axes, as shown in the following graphic.

The Robinson and Haggenmacher skew test uses the angle (alpha) between the edge 2 and edge 4 bisector and the test Y-axis. The resulting angle is subtracted from 90° to yield the skew angle.

Tetrahedral skew angle

For tetrahedral elements, each face is checked for skew as if it were a triangular element and retains the highest resulting angle for each element as the skew angle.

Wedge and hexahedral skew angle

For wedge and hexahedral elements, the software evaluates each face of the element for skew as if it were a quadrilateral or triangular element and retains the highest resulting angle for each element as the skew angle.

Quadrilateral taper

The Taper check measures the geometric deviation of a quadrilateral element from a rectangular shape.

Quadrilateral element taper is determined using a test proposed by Robinson and Haggenmacher. Four triangles are created bounded by the element edge and the edges created by connecting the element verification reference frame origin with the two nodes at the element edge. The resulting four triangular areas are calculated and summed. The ratio of the smallest triangular area to the total area of the element is the taper ratio:

taper ratio = 4*a(smallest)/a1+a2+a3+a4

Wedge and hexahedral taper

The software evaluates each face of a wedge or hexahedral element for taper as if it were a quadrilateral element. The software retains the highest resulting value for each element as the face taper value.

Jacobian

A Jacobian is a determinant used to describe the variance of some characteristic at two different positions in a system. For example, a Jacobian might be used to describe the variance of slope between two points on a curve. Jacobians are useful tools for measuring distortion. A Jacobian could be used to compare the orientation between two edges of an element.

The Jacobian measures the ratio between the area or volume of an element to the ideal parametric element. The software calculates this value by mapping a parent element (in computational space) against the actual element.

• The Jacobian Ratio check measures the ratio of the largest Jacobian determinant to the smallest. This ratio gives you an idea of overall distortion in an element. You can use the Jacobian Ratio check to identify when an element’s interior corner angles deviate too much from 90°. A Jacobian ratio close or equal to 1.0 is desired.

• The Jacobian Zero check calculates the determinant of the Jacobian (J) at all integration points for each element selected. The minimum value for each element is determined. You can use the Jacobian Zero check to identify incorrectly shaped elements. For a well formed element, J is positive at each integration point and is not significantly different from the J value at other integration points. J approaches zero as an element vertex angle approaches 180°. The Jacobian Zero value is the smallest determinant.

Where do I find it?

Application	Pre/Post
Prerequisite	A FEM, assembly FEM, or Simulation file as the work part and displayed part
Command Finder	Element Quality

Learn more

Evaluating element quality

Correcting 2D element quality failures

General geometry checks for elements

Nastran and Multiphysicselement quality checks

Abaqus element quality checks

ANSYS element quality checks

Samcef element quality checks (Simcenter Samcef)

LS-DYNA element quality checks

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Solver neutral element quality checks, Simcenter 3D 2021.1 Series

© 2020 Siemens

J. Robinson and G. W. Haggenmacher, "Element Warning Diagnostics,"

Finite Element News.

June and August, 1982

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